COT3100 Summer’2001 Assignment #1.(Solution key ) Assigned: 05/10, due: 05/22 before the lecture. Total 100pts. 1. a) (5pts) How many strings can be formed by ordering the letters ILLINOIS? ! 2 ! 3 ! 8 ⋅ b) (10pts) How many strings can be formed by ordering the letters ILLINOIS if some I appears before some L? 6 7 8 ! 2 ! 3 ! 8 ⋅ ⋅-⋅ 2. (5pts) In how many ways can 12 distinct books be divided among four students if each student gets three books? 3 ) ! 3 ( ! 12 3. (10pts) How many integer solutions of x 1 + x 2 + x 3 + x 4 =17 satisfy x 1 ≥ 0, x 2 ≥ 1, x 3 ≥ 2, x 4 ≥ 3? ! 3 ! 11 ! 14 ⋅ 4. Below is the list of properties that a group of people might possess. For each property, either give the minimum number of people that must be in a group to ensure that the property holds, or else indicate that the property need not hold even for arbitrary large groups of people. Assume that every year has exactly 365 days, ignore leap years. No proofs are required. a)

This preview
has intentionally blurred sections.
Sign up to view the full version.